Long-Memory Continuous Phase Modulation Turbo Detection Using Unitary Approximate Message Passing

Traditional continuous phase modulation (CPM) detection algorithms based on principal Laurent pulses suffer significant performance degradation in long-memory scenarios. To address this challenge, we propose a turbo-iterative detection scheme that treats the combined effects of Laurent pulses, matched filtering, and noise whitening as a virtual channel. With this treatment, unitary approximate message passing (UAMP) is employed to efficiently recover pseudo-symbols with complexity that remains independent of the CPM memory length. The proposed receiver jointly performs equalization, demodulation, and decoding in an iterative manner, leading to superior performance. Simulation results demonstrate that the proposed method significantly outperforms existing techniques under long-memory CPM conditions, particularly for high-order CPMs.